You will not hear me cue "exhale and press bellybutton to spine" in our Pilates classes. Why?
Firstly, this is not a very specific instruction and can be interpreted very differently by various people.
Secondly, on average, it tends to encourage squeezing everything tightly and holding the stomach in. As I wrote earlier, this does not give you good functional strength.
And thirdly, it can lead to people pushing the pressure from their exhale down onto their pelvic floor, or tensing their necks as compensations. All of these are not good strategies for our bodies.
Instead, I invite people to imagine exhaling as if they are drawing their out-breath up towards their chests away from their pelvic floors. Whilst doing that, we aim to keep ribs wide at the start of the exhale and not squeeze the air out at the initiation of the breath out.
There are other strategies to try. One more advanced one will be imagining that the lower belly is deepening and broadening outwards towards the spine, not inwards towards the bellybutton.
All these strategies aim to access the deeper stabilising abdominal muscles and not superficial ones like abdominal obliques or Rectus abdominis. It is the deeper muscle, called Transverse abdominis, that gives us true strength.